Interpreting canonical correlation analysis through biplots of structure correlations and weights

This paper extends the biplot technique to canonical correlation analysis and redundancy analysis. The plot of structure correlations is shown to the optimal for displaying the pairwise correlations between the variables of the one set and those of the second. The link between multivariate regression and canonical correlation analysis/redundancy analysis is exploited for producing an optimal biplot that displays a matrix of regression coefficients. This plot can be made from the canonical weights of the predictors and the structure correlations of the criterion variables. An example is used to show how the proposed biplots may be interpreted.     

COSMOLOGY FROM ALPHA TO OMEGA

Abstract. This paper focuses on four passages in the journey of the universe from beginning to end: its origin in the Big Bang, the production of heavy elements in first generation stars, the buzzing symphony of life on earth, and the distant future of the cosmos. As a physicist and a Christian theologian, I will ask how each of these passages casts light on the deepest questions of existence and our relation to God, and in turn how these questions are being explored through ongoing research into the interaction between Christian theology and the natural sciences.     

Processing reduced word forms: the suffix restoration effect

Listeners cannot recognize highly reduced word forms in isolation, but they can do so when these forms are presented in context (Ernestus, Baayen, & Schreuder, 2002). This suggests that not all possible surface forms of words have equal status in the mental lexicon. The present study shows that the reduced forms are linked to the canonical representations in the mental lexicon, and that these latter representations induce reconstruction processes. Listeners restore suffixes that are partly or completely missing in reduced word forms. A series of phoneme-monitoring experiments reveals the nature of this restoration: the basis for suffix restoration is mainly phonological in nature, but orthography has an influence as well.     

The Duty to Forgive Repentant Wrongdoers

Abstract

The purpose of this paper is to consider the question of whether we have a duty to forgive those who repent and apologize for the wrong they have done. I shall argue that we have a pro tanto duty to forgive repentant wrongdoers, and I shall propose and consider the norm of forgiveness. This norm states that if a wrongdoer repents and apologizes to a victim, then the victim has a duty to forgive the wrongdoer, other things being equal. That someone has a pro tanto duty to forgive a repentant wrongdoer means that he or she ought to forgive unless other considerations outweigh the norm of forgiveness. Furthermore, a distinction is made between what are termed ‘general considerations’ and ‘case‐relative considerations’, and it is argued that only after all the relevant considerations have been examined can it be determined whether there is a duty to forgive, all things considered.     

‘Black holes’: escaping the void

The ‘black hole’ is a metaphor for a reality in the psyche of many individuals who have experienced complex trauma in infancy and early childhood. The ‘black hole’ has been created by an absence of the object, the (m)other, so there is no internalized object, no (m)other in the psyche. Rather, there is a ‘black hole’ where the object should be, but the infant is drawn to it, trapped by it because of an intrinsic, instinctive need for a ‘real object’, an internalized (m)other. Without this, the infant cannot develop. It is only the presence of a real object that can generate the essential gravity necessary to draw the core of the self that is still in an undeveloped state from deep within the abyss. It is the moving towards a real object, a (m)other, that relativizes the absolute power of the black hole and begins a reformation of its essence within the psyche.     

Center of Gravity Motions and Ankle Joint Stiffness Control in Upright Undisturbed Stance Modeled Through a Fractional Brownian Motion Framework

The authors modeled the center of gravity vertical projection (CG_V) and the difference, CP - CG_V, which, combined, constitute the center of pressure (CP) trajectory, as fractional Brownian motion in order to investigate their relative contributions and t heir spatiotemporal articulation. The results demonstrated that CG_V and CP - CG_V motions are both endowed in complementary tashion with strong stochastic and part-deterministic behaviors. In addition, if the temporal coordinates remain similar for all 3 trajectories by definition, the switch between the successive control mechanisms appears for shorter displacements for CP - CG_V and CG_V than for CP trajectories. Results deduced from both input (CG,) and muscular stiffness (CP - CG_V) thus provide insight into the way the central nervous system regulates stance control and in particular how CG and CP - CG are controlled.     

Why We Walk the Way We Do

By using inverse dynamics and forceplate recordings, this study established the principle of oscillating systems and the influence of gravity and body parameters on the programming of the gait parameters, step frequency and length. Calculation of the ratio of the amplitude of the center of mass (CM) and the center of foot pressure (CP) oscillations yielded an equation and established a biomechanical constant, the natural body frequency (NBF). NBF appears to be an absolute invariant parameter, specific to human standing posture and gait in terrestrial gravity, which influences the relative positions of CM and CP and whose value separates the frequency bands of standing posture from those for gait. This equation was tested by using the experimental paradigm of stepping in place and then used in calculating the magnitude of CM oscillations during gait. The biomechanical analysis of the experimental observations allows one to establish the relationships between body parameters and gravity and the central programming of locomotor parameters.     

Preservation Theorems Without Continuum Hypothesis

Many results concerning the equivalence between a syntactic form of formulas and a model theoretic conditions are proven directly without using any form of a continuum hypothesis. In particular, it is demonstrated that any reduced product sentence is equivalent to a Horn sentence. Moreover, in any first order language without equality one now has that a reduced product sentence is equivalent to a Horn sentence and any sentence is equivalent to a Boolean combination of Horn sentences.     

Prerequisites to Human Activity on Mars: Scientific and Ethical Aspects

Humans want to go to Mars now. This entails many difficult but solvable challenges. However, human activity on Mars depends on the answers to three fundamental questions: (1) Is there life on Mars, does that life represent at second genesis of life? (2) Can Earth life, and humans in particular, adapt to the Martian gravity of 0.38?g, and will human generations on Mars speciate from humans on Earth? (3) Is there enough carbon, nitrogen, and water on Mars to create a global habitable environment? These answers must be determined on Mars and will decide the scope of human activities.     

The Internal and External Problems of String Theory: A Philosophical View

String theory is at the moment the only advanced approach to a unification of all interactions, including gravity. But, in spite of the more than 30 years of its existence, it does not make any empirically testable predictions, and it is completely unknown which physically interpretable principles could form the basis of string theory. At the moment, “string theory” is no theory at all, but rather a labyrinthic structure of mathematical procedures and intuitions. The only motivations for string theory consist in the mutual incompatibility of the standard model of quantum field theory and of general relativity as well as in the metaphysics of the unification program of physics, aimed at a final unified theory of all interactions, including gravity. The article gives a perspective on the problems leading to and resulting from this situation.